Explanation:

- To solve the problem, understand it's about finding a least common number (LCM issue) with a remainder pattern.

- You need the smallest number \( x \) such that:

- \( x \equiv 5 \pmod{72} \)

- \( x \equiv 5 \pmod{96} \)

- In simpler terms: When you subtract 5 from this number, it should be divisible by both 72 and 96.

- LCM of 72 and 96 helps here, which is 288.

- Add 5 to a multiple of this LCM for correct remainder.

- Options checked:

- Option 1: 283 — Subtracting 5 gives 278, not a solution.

- Option 2: 571 — Subtracting 5 gives 566, not a solution.

- Option 3: 581 — Subtracting 5 gives 576, a multiple of 288.

- Option 4: 293 — Subtracting 5 gives 288, a multiple of 288.

- Correct answer is Option 4: 293.

.